A Monte Carlo Resampling Approach for the Calculation of Hybrid Classical and Quantum Free Energies
A Monte Carlo Resampling Approach for the Calculation of Hybrid Classical and Quantum Free Energies
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DOI：
10.1021/acs.jctc.6b00506
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发表时间：
2017-02-01
影响因子：
5.5
通讯作者：
Essex, Jonathan W.
中科院分区：
文献类型：
--
作者：
Cave-Ayland, Christopher;Skylaris, Chris-Kriton;Essex, Jonathan W.
混合自由能方法允许通过在经典力学 (MM) 级别执行采样来高效估计量子力学 (QM) 级别的自由能差异。已经提出了各种允许计算经典自由能的 QM 校正的方法。单步自由能扰动方法从经典生成的系综开始，对系综的结构子集进行后处理以获得用于 Zwanzig 方程的 QM 能量。这给出了与从 MM 到 QM 哈密顿量的变化相关的自由能差的估计。然而，由于 Zwanzig 方程的数值性质较差，最近的发展产生了替代方法，旨在提供真正的 QM 系综的性质。在这里，我们提出了一种基于 MM 结构系综重采样和蒙特卡罗验收测试应用的方法，原则上可以生成精确的 QM 系综或 MM 和 QM 状态之间的中间系综。我们对 Zwanzig 方程和最近提出的非玻尔兹曼方法进行了详细的比较。作为测试系统，我们使用一组小分子水合自由能，在半经验密度泛函紧结合水平上进行混合自由能计算。还生成了该理论水平的等效系综，允许执行反向 QM 到 MM 扰动以及对结果的详细分析。此外，还考虑了使用从头算分子动力学在 QM 水平模拟的先前发布的核苷酸碱基对数据集。我们通过证明可以估计配置空间重叠来提供使用蒙特卡洛重采样和非玻尔兹曼方法的强有力的理由，这提供了有关这些混合方法准确性的有用诊断信息。
Hybrid free energy methods allow estimation of free energy differences at the quantum mechanics (QM) level with high efficiency by performing sampling at the classical mechanics (MM) level. Various approaches to allow the calculation of QM corrections to classical free energies have been proposed. The single step free energy perturbation approach starts with a classically generated ensemble, a subset of structures of which are postprocessed to obtain QM energies for use with the Zwanzig equation. This gives an estimate of the free energy difference associated with the change from an MM to a QM Hamiltonian. Owing to the poor numerical properties of the Zwanzig equation, however, recent developments have produced alternative methods which aim to provide access to the properties of the true QM ensemble. Here we propose an approach based on the resampling of MM structural ensembles and application of a Monte Carlo acceptance test which in principle, can generate the exact QM ensemble or intermediate ensembles between the MM and QM states. We carry out a detailed comparison against the Zwanzig equation and recently proposed non-Boltzmann methods. As a test system we use a set of small molecule hydration free energies for which hybrid free energy calculations are performed at the semiempirical Density Functional Tight Binding level. Equivalent ensembles at this level of theory have also been generated allowing the reverse QM to MM perturbations to be performed along with a detailed analysis of the results. Additionally, a previously published nucleotide base pair data set simulated at the QM level using ab initio molecular dynamics is also considered. We provide a strong rationale for the use of the Monte Carlo Resampling and non-Boltzmann approaches by showing that configuration space overlaps can be estimated which provide useful diagnostic information regarding the accuracy of these hybrid approaches.